Finding the limit of a recursive sequence. – math.stackexchange.com

Let $a_n \in \Bbb{R}$ such that: $$ a_{n+1}=1+\frac{2}{a_n} \text{ and } a_1=1$$ Prove that $\lim_{n \to +\infty}a_n=2$ We have that $a_n \geq 1,\forall n \in \Bbb{N}$ thus $$\limsup_na_n ...

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